On the IAA version of the Doi–Edwards model versus the K-BKZ rheological model for polymer fluids: A global existence result for shear flows with small initial data

Abstract

This paper establishes the existence of smooth solutions for the Doi-Edwards rheological model of viscoelastic polymer fluids in shear flows. The problem turns out to be formally equivalent to a K-BKZ equation but with constitutive functions spanning beyond the usual mathematical framework. We prove, for small enough initial data, that the solution remains in the domain of hyperbolicity of the equation for all t ≥ 0.

Solvability for a drift-diffusion system with Robin boundary conditions

“…When coupled with fluid flows equations, the resulting systems are usually quite complex due to the micro-macro effect. A short reference list is [8,9,10,11,15,22] for some problems arising in different contex, including the theory of dilute or melt polymers. Apart from the theory of stochastic process -mainly the Fokker-Planck equation -a priviledged field of application is the theory of semi conductors.…”

New Temperature Dependent Configurational Probability Diffusion Equation For Diluted FENE Polymer Fluids: Existence of Solution Results

“…As to the second goal, the importance of studying the full system of equations consisting of momentum balance CPD (and of the closely related stress tensor) and the heat diffusion equations notwithstanding (see for instance [17], [15], [1], [2], [5]), it is to be noted here that it is common matter in the rheology literature (as per [4], [20], [25]) to first focus on the CPD alone, see e.g. [5], [6], [7], [8], [9], [10] - [13], [22].…”